The invention relates to a method for homogenizing the static magnetic field with a distribution B0(r) in the active volume of a magnetic resonance apparatus having a number N shim coils, wherein the method comprises the following steps:                (a) Mapping the magnetic field distribution B0(r) of the static magnetic field,        (b) Defining a target field distribution B0T(r),        (c) Generating the target field distribution B0T(r) in the active volume by adjusting currents in the shim coils,        
wherein an optimization procedure for optimizing a numerical quality criterion for the target field distribution B0T(r) is used in step (b),
wherein the optimization procedure supplies, as a result, values for the currents through the N shim coils,
and wherein a spatial weighting function is used in the optimization method.
Such a method is known from Markus Weiger, Thomas Speck, Michael Fey, “Gradient Shimming with Spectrum Optimization,” Journal of Magnetic Resonance 182 (2006), 38-48 (=reference [5]).
Many magnetic resonance methods require static magnetic fields to be as homogeneous as possible, for example, in order to achieve a high spectral resolution in the case of a spectroscopic method or to achieve an image that is as free of distortions and as sharp as possible in the case of an imaging method. So-called shim coils are a known means for adjusting the homogeneity of the static magnetic field (see reference [2], for example), making available magnetic fields that are adjustable in the active volume in addition to the main magnetic field. Each of these shim coils is supplied with electric current from its own adjustable current source. A broad range of field distributions can be homogenized by means of the different field distributions generated by the various shim coils. Shim systems with up to 38 independent shim coils, or correspondingly the current sources, are already known.
In addition to the apparatus for generating the magnetic fields, a method for finding the suitable current setting is required. Such a method, by application of which the desired homogeneous magnetic field distribution in the working volume is achieved, is known as a shimming method. One particular difficulty with such methods involves the handling of the large number of degrees of freedom in the choice of the current setting. In particular, well-known shimming methods (for example, see reference [1]), that incrementally improve a measured variable used for capturing the global homogeneity, such as the amplitude, the signal energy or the second moment of a resonance line, by performing minor changes in each degree of current freedom, suffer from an enormous increase in the number of process steps required with an increase in the number of degrees of freedom.
A significant improvement in comparison with such a method is achieved when the shimming method takes into account information about the spatial distribution of the static magnetic field in the active volume. Information about the spatial distribution of the static magnetic field is obtained in a process step in which the magnetic field distribution B0(r) of the static magnetic field is mapped with the help of a suitable measurement method.
Known methods for adjusting the currents in the shim coils that are particularly efficient comprise the following steps:                (a) Mapping the magnetic field distribution B0(r) of the static magnetic field,        (b) Defining a target field distribution B0T(r)        (c) Generating the target field distribution B0T(r) in the active volume by adjusting the currents through the shim coils.        
Such a method is described in reference [4]:
The magnetic field distribution B0(r) is mapped in the active volume of the static magnetic field by means of a method based on phase-sensitive magnetic resonance imaging, the application of which uses switchable gradient coils for determining the spatial origin of the signals. Examples of such methods include the gradient-echo method and the spin-echo method.
A quality criterion whose optimum value (minimum or maximum) defines the target field distribution B0T(r) is used in defining the target field distribution B0T(r). A quality criterion derived from a simulated spectrum is used in the method according to reference [4]. Properties such as the full width at half height (FWHH) of spectral lines and envelope curves around spectral lines are determined on this predicted spectrum and are combined to form a variable, which serves as the target variable for an optimization algorithm. After the optimization algorithm has found an optimum for this target variable, the magnetic field distribution belonging to this optimum is defined as the target field distribution. Then in this method, the currents in the shim coils are adjusted iteratively and the effect achieved thereby is verified by renewed mapping of the magnetic field distribution in the active volume until the target field distribution is reached.
There are many known optimization algorithms suitable for finding the target field distribution. Options include the Gaussian-Newtonian method, the conjugated gradient method, the simplex method and the simulated annealing method. In general, there is an increase in the computation effort for discovering an optimum with a higher dimensionality of the parameter space, in this case with the number of shim coils or correspondingly the number of currents.
The most proximate prior art to the subject matter of the present invention is described in reference [5] cited in the introduction.
Here also, optimization of a quality criterion is performed to define the target field distribution, whereby a spatial weighting function is used in the optimization method. Efficient optimization is achieved by reducing the parameter space to one dimension. Optimization in a one-dimensional parameter space is implemented here, such that the measured magnetic field distribution B0(r) is subjected to a weighted fit with a spatial weighting function W(r, k)=(B1(r))k wherein the exponent k is changed. The fit functions here are the field distributions of the shim coils. The role of the single parameter is taken over by k. Each choice of the parameter k leads to a list of currents to be set for the shim coils and to a field distribution, which is close to a homogeneous distribution.
A small number of analyses (i.e., a small number of values for k) are often sufficient to find a very good solution, even when there is no guarantee that it will be the optimum solution. The advantage of this procedure is in avoiding the optimization with as many dimensions as there are shim coils in a high-dimensional parameter space.
A further problem with shimming methods is based on the fact that the approximation of a magnetic field distribution, as obtained by mapping the field distribution in the active volume, using a set of field distributions, such as those that can be created by the shim coils, generally leads to a mathematically ill-posed problem. The known approach of handling problems that are mathematically ill-posed is by regularization of the problems (see reference [6], for example).
These problems can be largely eliminated by means of regularization, where an attempt is made to prevent high-frequency oscillations with the smallest possible filter effect. One application for regularizing the shimming of MRI experiments is described in reference [3]. The shimming method described there is aimed at eliminating the numeric instabilities, which occur when an active volume that is not spherical and whose center is shifted with respect to the midpoint of the shim coils is to be shimmed using shim coils that are constructed such that the magnetic fields generated by them form an orthogonal function set in a spherical volume around a midpoint (see reference [3], column 1, lines 56-63).
In this case, if shimming is done using high-order functions (i.e., a large number of degrees of freedom of the current are determined), then even minor errors that occur due to measurement noise, for example, will affect the mapped magnetic fields, so that the result will be excessive shimming currents with opposite signs as an unusable solution, unless regularization is performed. Divergence of the currents can be prevented by using a regularization method.
Although the problems described in the last section with divergent currents may not occur in all cases, it is of great interest in general to find shim current settings that are economical with respect to shimming power. The reasons for this include preventing heating of the measurement system and of the sample volume by the neighboring shim coils. In addition, it is advantageous to operate the current sources with currents at sufficient distance away from hardware limitations. In addition to maximum values for the individual currents, the total power of the power supply for the current sources, as well as the temperature of electronic elements, are relevant limitations.
A restriction of the optimization to a one-dimensional parameter space, as described in reference [5] is too restrictive to take into account such hardware limitations in the current or power. However, explicitly taking these limitations into account in turn requires that the parameter space in its full size must be taken into account, which results in an optimization that is too time consuming.
One very primitive way to take into account current limitations consists simply of first calculating an optimization of the quality criterion without taking the limitation into account and then capping the individual currents for the shim coils at the respective maximum allowed value. As shown in reference [7], a better result can be achieved in general with the same limitations. The improvement proposed in reference [7] employs a minimization algorithm, that is tailored to the specific case of one positive limit and one negative limit for each individual shimming current and a quadratic dependence of the quality criterion on the shimming currents. As discussed above, more complex limitations such as shimming power also play a role in practice. Quality criteria, whose dependence on the shimming currents is different from a quadratic dependence, would also be desirable. In both of these cases, the algorithm can no longer be applied. Furthermore, the parameter space of the shim currents is taken into account in its full size in the minimization algorithm proposed in reference [7].
In contrast thereto, the application of a regularization method allows at least an indirect influence on the shimming power. However, the optimally regularized solutions do not provide any information about the quality of the shimming state as a function of the shimming current efficiency. There are often many other solutions that yield a comparable shimming quality but use much less power.
The present invention is thus based on the object of providing a method of the type defined in the introduction, in which the hardware limitations are taken into account in determining the target field distribution without any significant increase in the computation effort in optimization to determine the target field distribution.
In addition, the invention should have the effect that more points in the parameter space are tested to thereby reduce the probability that the proximity to the optimum solution is missed. The increase of the number of points in the parameter space shall be used to explore an independent direction.